Details

Time bar (total: 5.0s)

sample36.0ms

Algorithm
intervals
Results
8.0ms254×body80nan
7.0ms59×body1280valid
5.0ms126×body80valid
4.0ms43×body640valid
1.0ms17×body320valid
1.0ms11×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.4b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
54×*-un-lft-identity
42×add-sqr-sqrt prod-diff
31×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
4×add-log-exp difference-of-squares
3×pow1 distribute-lft-out--
2×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+ hypot-def
Counts
2 → 89
Calls
2 calls:
4.0ms
(sqrt (+ x 1.0))
27.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series103.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(sqrt (+ x 1.0))
72.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify42.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02991161
1921822
25001744

prune144.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
33×distribute-lft-out
32×sqrt-prod
24×times-frac
21×add-sqr-sqrt
18×add-cube-cbrt
7×fma-def
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 flip3-+ flip-+ associate-/l*
3×expm1-log1p-u log1p-expm1-u
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log hypot-def div-inv
Counts
3 → 94
Calls
3 calls:
4.0ms
(sqrt (+ x 1.0))
21.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
29.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series247.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(sqrt (+ x 1.0))
69.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
141.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify53.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0409789
11675716
25001675

prune223.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x 1.0)))
0.1b
(sqrt (sqrt (+ x 1.0)))
0.1b
(fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x))
0.1b
(/ (+ 1.0 0) (fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity
24×sqrt-prod
21×add-sqr-sqrt
17×add-cube-cbrt
12×times-frac
8×pow1 sqrt-pow1 sqrt-div
6×add-exp-log add-cbrt-cube distribute-lft-out
4×expm1-log1p-u rem-sqrt-square pow1/2 log1p-expm1-u associate-/l* add-log-exp
3×flip3-+ associate-/r* flip-+
2×associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
4 → 93
Calls
4 calls:
4.0ms
(sqrt (sqrt (+ x 1.0)))
4.0ms
(sqrt (sqrt (+ x 1.0)))
0.0ms
(fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x))
8.0ms
(/ (+ 1.0 0) (fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x)))

series724.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(sqrt (sqrt (+ x 1.0)))
92.0ms
(sqrt (sqrt (+ x 1.0)))
225.0ms
(fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x))
317.0ms
(/ (+ 1.0 0) (fma (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))) (sqrt x)))

simplify82.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
07431316
132361218
250031183

prune330.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite258.0ms

Algorithm
rewrite-expression-head
Rules
597×*-un-lft-identity
420×sqrt-prod
256×distribute-lft-out
247×times-frac
130×add-sqr-sqrt
99×add-cube-cbrt
71×swap-sqr
33×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 flip3-+ pow1/2 flip-+ unswap-sqr
8×associate-/l*
7×div-inv
5×sqrt-div pow-prod-up
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 324
Calls
4 calls:
29.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
31.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
29.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
140.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series817.0ms

Counts
4 → 12
Calls
4 calls:
353.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
149.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
141.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
174.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify135.0ms

Algorithm
egg-herbie
Counts
336 → 336
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
07233900
137333364
250023360

prune594.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes32.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01210
11610
21610

end0.0ms

sample1.0s

Algorithm
intervals
Results
269.0ms8128×body80nan
224.0ms1778×body1280valid
155.0ms4098×body80valid
124.0ms1218×body640valid
45.0ms571×body320valid
21.0ms335×body160valid